Prepare the Cake Preheat oven to 350°F. Coat 2 (9-inch) round cake pans with baking spray; line bottoms using parchment paper.

Beat sugar, butter, and oil with a stand mixer fitted with a paddle attachment on medium speed until fluffy, about 2 minutes, stopping to scrape down sides as needed. Add eggs, 1 at a time, beating until combined after each addition, 15 to 30 seconds. Beat in vanilla bean paste, about 10 seconds.

Sift together flour, baking powder, salt, and baking soda into a medium bowl. Whisk together milk and sour cream in a small bowl until smooth and well combined. With mixer on low speed, gradually add flour mixture to sugar mixture in mixer, alternately with milk mixture, beginning and ending with flour mixture, beating until combined, 2 to 3 minutes. Divide batter evenly between prepared cake pans (about 3 ½ cups each), spreading into an even layer. Tap cake pans on a kitchen towel-lined countertop several times to release any large bubbles.

Bake in preheated oven until a wooden pick inserted into center of cakes comes out clean with a few moist crumbs, 32 to 35 minutes. Let cool in cake pans on a wire rack for 10 minutes. Remove cakes from pans, and let cool completely on a wire rack, about 2 hours. Carefully trim cake layers flat, if needed, using a sharp serrated knife.

Prepare the Frosting Microwave chocolate and espresso powder in a large, microwavable bowl on HIGH in 15- to 30-second intervals, stirring between each interval, until melted and smooth, about 1 ½ to 2 ½ minutes. Let cool 10 minutes, stirring occasionally.

While chocolate cools, process powdered sugar, butter, cocoa, and salt in a food processor until smooth, about 1 minute, stopping to scrape down sides as needed. Add corn syrup and vanilla bean paste; process until smooth, about 30 seconds. Add cooled chocolate; process until smooth, about 30 seconds. (If Frosting seems too loose, refrigerate uncovered in 5 to 10 minute intervals, stirring occasionally, until desired consistency is reached.)

Remove and discard parchment paper. Place 1 Cake layer on a plate. Spread 1 cup Frosting over top. Top with second Cake layer. Spread Frosting over top and sides of Cake as desired.